In a large mixing bowl or the bowl of a stand mixer, thoroughly stir together the all purpose flour, milk, starter, honey, and butter. Cover the bowl with a clean cloth and allow it to sit for 30 minutes to an hour to create a sponge.
 

Add the bread flour and salt and stir until completely combined. If using a stand mixer, use the dough hook. If mixing by hand, use a sturdy large spoon or a bowl scraper to stir. Work the dough until it is completely combined, then knead it for 5-8 minutes (with the mixer) or 8-10 minutes (by hand) to create a smooth, elastic dough. Grab a small bit off the edge of the ball and gently pull up on it. If the fibers tear quickly, keep kneading. However, if they stretch and pull smoothly, your dough is ready.

 Form the dough into a smooth ball and place it in a clean bowl. Recover it with the cloth and allow it to sit at room temperature for 3-4 hours, or until it has puffed up and is soft to the touch. It doesn’t necessarily need to double in size, but should keep an indent when you press gently on it with your finger. 

Cooking the English Muffins:

After the dough has risen, you can put it in the refrigerator overnight or roll and cook the muffins immediately. Sprinkle a clean surface with the cornmeal or semolina flour, and use a rolling pin to roll the dough out to a little over ½” thick. Use a biscuit cutter (or a wide mouth jar ring like me, because faaaannncy) to cut out rounds between 3”-4”. Set each one on a parchment lined baking sheet, cover with a clean kitchen towel, and allow them to rise for 1-2 hours, depending on the temperature of your kitchen and the starting temperature of the dough.

 
About 10-15 minutes before you are ready to cook, begin to heat your griddle on medium low. Allow it to heat slowly. You know it is ready when you wet your fingers, flick them at the griddle, and the water droplets dance and fizzle on the surface. Sprinkle with a light layer of cornmeal or semolina, the place as many of the risen muffins on the griddle as you can without allowing them to touch.
 

Cook for 7-9 minutes on each side, or until both sides are nicely toasted and crispy. Insert an internal thermometer into the soft sides to measure the internal temperature and make sure it’s done. It should read 180F when the centers are cooked through.